A new approximation for peak transient dynamic displacements is presen
ted. This approximation is based on modal analysis and is valid for ge
neral damped structures, which includes the case of actively controlle
d structures. Intermediate design variable and intermediate response q
uantity concepts are used to enhance the accuracy of the approximation
. When this high-quality approximation is used within the context of t
he approximation concepts approach to design synthesis, the overall ef
ficiency of the process expected to be improved by reducing the number
of complete analyses required for convergence. Numerical results that
illustrate the effectiveness of the method are presented.